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In atomic, molecular, and optical physics and quantum chemistry, the molecular Hamiltonian is the Hamiltonian operator representing the energy of the electrons and nuclei in a molecule. This operator and the associated Schrödinger equation play a central role in computational chemistry and physics for computing properties of molecules and aggregates of molecules, such as thermal conductivity, specific heat, electrical conductivity, optical, and magnetic properties, and reactivity.
One of the guiding principles in modern chemical dynamics and spectroscopy is that the motion of the nuclei in a molecule is slow compared to that of its electrons. This is justified by the large disparity between the mass of an electron, and the typical mass of a nucleus and leads to the Born–Oppenheimer approximation and the idea that the structure and dynamics of a chemical species are largely determined by nuclear motion on potential energy surfaces. The potential energy surfaces are obtained within the adiabatic or Born–Oppenheimer approximation.
In quantum chemistry, a conical intersection of two or more potential energy surfaces is the set of molecular geometry points where the potential energy surfaces are degenerate (intersect) and the non-adiabatic couplings between these states are non-vanishing. In the vicinity of conical intersections, the Born–Oppenheimer approximation breaks down and the coupling between electronic and nuclear motion becomes important, allowing non-adiabatic processes to take place.
Ehrenfest dynamics is a useful approximation for ab initio mixed quantum-classical molecular dynamics that can treat electronically nonadiabatic effects. Although a severe approximation to the exact s
Accurate simulations of molecular quantum dynamics are crucial for understanding numerous natural processes and experimental results. Yet, such high-accuracy simulations are challenging even for relat
Diabatization of the molecular Hamiltonian is a standard approach to remove the singularities of nonadiabatic couplings at conical intersections of adiabatic potential energy surfaces. In general, it